## Evaluate integral

### Description

This function will evaluate the integral in equation (4) on page 7 of the paper. See Details section.

### Usage

 1 integrate2(limit.vec = c(-3, 3), theta.diff, sigma.2 = 1, n = 1) 

### Arguments

 limit.vec This is a vector of length 2. It consists of the lower and upper limits in the integral. Checking is carried out to ensure that is of length two, and that limit.vec[1] <= limit.vec[2]. theta.diff A vector of length p-1, where p is the number of populations of treatments. Coordinate [i] in theta.diff corresponds to θ_i - θ_{i+1}. See genDelMat. sigma.2 The known variance of the error terms. n The number of replications per population.

### Details

This function evaluates the integral, and works with the lower and upper limits that it is given. If one desires to compute the coverage probability for an interval defined by X_{(1)} \pm c, then the user should look at the function exactCoverageProb in this package.

### Value

The function returns a scalar value that is the value of the integral in equation (4) of page 7, defined by the lower and upper limits provided here.

exactCoverageProb, integrand

### Examples

 1 2 del1 <- c(2, 4) integrate2(c(-1.1,1.3), del1) 

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